src/ZF/ex/TermFn.thy

theorems [cases type: bool] = case_split;

(*  Title: 	ZF/ex/term-fn.thy
    ID:         $Id$
    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   1993  University of Cambridge

Terms over an alphabet.
Illustrates the list functor (essentially the same type as in Trees & Forests)
*)

TermFn = Term + ListFn +
consts
    term_rec    :: "[i, [i,i,i]=>i] => i"
    term_map    :: "[i=>i, i] => i"
    term_size   :: "i=>i"
    reflect     :: "i=>i"
    preorder    :: "i=>i"

rules
  term_rec_def
   "term_rec(t,d) == \
\   Vrec(t, %t g. term_case(%x zs. d(x, zs, map(%z.g`z, zs)), t))"

  term_map_def	"term_map(f,t) == term_rec(t, %x zs rs. Apply(f(x), rs))"

  term_size_def	"term_size(t) == term_rec(t, %x zs rs. succ(list_add(rs)))"

  reflect_def	"reflect(t) == term_rec(t, %x zs rs. Apply(x, rev(rs)))"

  preorder_def	"preorder(t) == term_rec(t, %x zs rs. Cons(x, flat(rs)))"

end